If it were mine, I'd swap the flywheel and clutch for the larger 12volt ones, and change the oil seal while the flywheel's off too.
You would need to swap the electical bits on the enginge for 12v parts too, including choke element on the carb and the coil etc.
Or you could just run with a 6 volt starter. You would need the change the bronze bush in the bell housing to fit it and it would turn over faster running on 12 volts! This is NOT the right way to go about it, but it does work. This would reduce the life of the starter though. 😃